I can think of two main reasons why cats lie on books. The first is because the book is a hard surface. And if the book is on a bed, which it is likely to be, it is surrounded by soft surfaces. The book is going to be cooler than the duvet cover which is an insulator trapping air. Actually, it feels cooler to both humans and to your cat. The science behind this is complicated. But essentially I believe it is because harder surface conduct heat better. Therefore when you touch a hard surface heat flows from you into the hard surface so it feels colder. The same sensation will be experienced by a cat but less so because they are covered with fur. Notwithstanding that, they are very sensitive and can feel heat or cold through their fur. So the first reason is that a book is cooler than bedclothes, in this example.
I would expect, therefore, a cat to sleep or rest on a book if they are on your bed in warm weather. The desire to lie on a book rather than a warmer surface such as bedding can only happen if the ambient temperature is a little uncomfortably warm for a cat or because he has come in from the outside where he was lying in hot sun. He comes in to cool off. He may lie on a hard kitten floor as an alternative.
But there is an additional reason which overlaps with the first. This is because books have been handled by you, a cat owner. Your scent is on the book. Your cat wants to mingle his scent with yours. This is called “scent exchange”. Your scent is transferred to him and his scent is transferred to the book. It is almost as if he is claiming ownership of the book with you. It becomes a shared object and in sharing a cat feels more secure.
So the two reasons are linked by the emotion of feeling better. Your cat feels better because he feels cooler and your cat feels better because he feels reassured.
There is a potential third reason which I’m not sure about that which may occur sometimes. If you are preoccupied with reading a book and as a consequence ignore your cat who is nearby and in need of attention, he may lie on the book when you put it down to stop you reading it. This is called attention seeking. I’m not convinced that cats are that determined about attention seeking. They ask for attention with the meow, we know about that of course, but to stop a person using an object in order to get their attention, that is another matter.
There are two pictures on this page. One is of my cat who lay down on my book, actually an instruction manual for my car, because it was a cooler surface than the surrounding bed. And the other is of a 16-year-old ginger tabby-and-white cat living with Sarah Hepola who was writing for The Dodo website. She said that her cat rubbed his cheek against the book as well. This supports the idea of scent exchange mentioned above. It is an added behaviour to ensure that scent exchange takes place.